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Scalarization of Henig Proper Efficient Points in a Normed Space

Author

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  • X. Y. Zheng

    (Yunnan University)

Abstract

In a general normed space equipped with the order induced by a closed convex cone with a base, using a family of continuous monotone Minkowski functionals and a family of continuous norms, we obtain scalar characterizations of Henig proper efficient points of a general set and a bounded set, respectively. Moreover, we give a scalar characterization of a superefficient point of a set in a normed space equipped with the order induced by a closed convex cone with a bounded base.

Suggested Citation

  • X. Y. Zheng, 2000. "Scalarization of Henig Proper Efficient Points in a Normed Space," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 233-247, April.
    • Handle: RePEc:spr:joptap:v:105:y:2000:i:1:d:10.1023_a:1004626414839
    DOI: 10.1023/A:1004626414839
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    Cited by:

    1. Fernando García-Castaño & Miguel Ángel Melguizo-Padial & G. Parzanese, 2023. "Sublinear scalarizations for proper and approximate proper efficient points in nonconvex vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(3), pages 367-382, June.
    2. J. H. Qiu & Y. Hao, 2010. "Scalarization of Henig Properly Efficient Points in Locally Convex Spaces," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 71-92, October.
    3. P. Q. Khanh & N. D. Tuan, 2008. "Higher-Order Variational Sets and Higher-Order Optimality Conditions for Proper Efficiency in Set-Valued Nonsmooth Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 243-261, November.

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